Speaker:

Baruch Meerson

Title:

Spectral Theory of Large Deviations in Birth-Death Systems

Abstract:

We suggest a simple and general spectral method [1-3] for calculating the extreme statistics of a broad class of (not necessarily single-step) birth-death processes and chemical reactions involving a single species.  The method employs the well-known generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. For extinction problems the method yields accurate results for the extinction statistics and for the quasi-stationary probability distribution, including large deviations, of the metastable state. I will demonstrate the power of the method on the example of a branching and annihilation reaction, A →2A; 2A→Ø; representative of a rather general class of processes. If time permits, I will also discuss a simple two-species model that exhibits an unexpected effect of noise enhanced stability.

References
[1] M. Assaf and B. Meerson, Phys. Rev. Lett. 97, 200602 (2006).
[2] M. Assaf and B. Meerson, Phys. Rev. E 74, 041115 (2006).
[3] M. Assaf and B. Meerson, Phys. Rev. E (to appear); cond-mat/0612157.

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